/usr/share/gocode/src/github.com/remyoudompheng/bigfft/fermat.go is in golang-github-remyoudompheng-bigfft-dev 0.0~git20130913.0.a8e77dd-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 | package bigfft
import (
"math/big"
)
// Arithmetic modulo 2^n+1.
// A fermat of length w+1 represents a number modulo 2^(w*_W) + 1. The last
// word is zero or one. A number has at most two representatives satisfying the
// 0-1 last word constraint.
type fermat nat
func (n fermat) String() string { return nat(n).String() }
func (z fermat) norm() {
n := len(z) - 1
c := z[n]
if c == 0 {
return
}
if z[0] >= c {
z[n] = 0
z[0] -= c
return
}
// z[0] < z[n].
subVW(z, z, c) // Substract c
if c > 1 {
z[n] -= c - 1
c = 1
}
// Add back c.
if z[n] == 1 {
z[n] = 0
return
} else {
addVW(z, z, 1)
}
}
// Shift computes (x << k) mod (2^n+1).
func (z fermat) Shift(x fermat, k int) {
if len(z) != len(x) {
println(len(z), len(x))
panic("len(z) != len(x) in Shift")
}
n := len(x) - 1
// Shift by n*_W is taking the opposite.
k %= 2 * n * _W
if k < 0 {
k += 2 * n * _W
}
neg := false
if k >= n*_W {
k -= n * _W
neg = true
}
kw, kb := k/_W, k%_W
z[n] = 1 // Add (-1)
if !neg {
for i := 0; i < kw; i++ {
z[i] = 0
}
// Shift left by kw words.
// x = a·2^(n-k) + b
// x<<k = (b<<k) - a
copy(z[kw:], x[:n-kw])
b := subVV(z[:kw+1], z[:kw+1], x[n-kw:])
if z[kw+1] > 0 {
z[kw+1] -= b
} else {
subVW(z[kw+1:], z[kw+1:], b)
}
} else {
for i := kw + 1; i < n; i++ {
z[i] = 0
}
// Shift left and negate, by kw words.
copy(z[:kw+1], x[n-kw:n+1]) // z_low = x_high
b := subVV(z[kw:n], z[kw:n], x[:n-kw]) // z_high -= x_low
z[n] -= b
}
// Add back 1.
if z[0] < ^big.Word(0) {
z[0]++
} else {
addVW(z, z, 1)
}
// Shift left by kb bits
shlVU(z, z, uint(kb))
z.norm()
}
// ShiftHalf shifts x by k/2 bits the left. Shifting by 1/2 bit
// is multiplication by sqrt(2) mod 2^n+1 which is 2^(3n/4) - 2^(n/4).
// A temporary buffer must be provided in tmp.
func (z fermat) ShiftHalf(x fermat, k int, tmp fermat) {
n := len(z) - 1
if k%2 == 0 {
z.Shift(x, k/2)
return
}
u := (k - 1) / 2
a := u + (3*_W/4)*n
b := u + (_W/4)*n
z.Shift(x, a)
tmp.Shift(x, b)
z.Sub(z, tmp)
}
// Add computes addition mod 2^n+1.
func (z fermat) Add(x, y fermat) fermat {
if len(z) != len(x) {
panic("Add: len(z) != len(x)")
}
addVV(z, x, y) // there cannot be a carry here.
z.norm()
return z
}
// Sub computes substraction mod 2^n+1.
func (z fermat) Sub(x, y fermat) fermat {
if len(z) != len(x) {
panic("Add: len(z) != len(x)")
}
n := len(y) - 1
b := subVV(z[:n], x[:n], y[:n])
b += y[n]
// If b > 0, we need to subtract b<<n, which is the same as adding b.
z[n] = x[n]
if z[0] <= ^big.Word(0)-b {
z[0] += b
} else {
addVW(z, z, b)
}
z.norm()
return z
}
func (z fermat) Mul(x, y fermat) fermat {
n := len(x) - 1
if n < 30 {
z = z[:2*n+2]
basicMul(z, x, y)
z = z[:2*n+1]
} else {
var xi, yi, zi big.Int
xi.SetBits(x)
yi.SetBits(y)
zi.SetBits(z)
zb := zi.Mul(&xi, &yi).Bits()
if len(zb) <= n {
// Short product.
copy(z, zb)
for i := len(zb); i < len(z); i++ {
z[i] = 0
}
return z
}
z = zb
}
// len(z) is at most 2n+1.
if len(z) > 2*n+1 {
panic("len(z) > 2n+1")
}
i := len(z) - (n + 1) // i <= n
c := subVV(z[1:i+1], z[1:i+1], z[n+1:])
z = z[:n+1]
z[n]++ // Add -1.
subVW(z[i+1:], z[i+1:], c)
// Add 1.
if z[n] == 1 {
z[n] = 0
} else {
addVW(z, z, 1)
}
z.norm()
return z
}
// copied from math/big
//
// basicMul multiplies x and y and leaves the result in z.
// The (non-normalized) result is placed in z[0 : len(x) + len(y)].
func basicMul(z, x, y fermat) {
// initialize z
for i := 0; i < len(z); i++ {
z[i] = 0
}
for i, d := range y {
if d != 0 {
z[len(x)+i] = addMulVVW(z[i:i+len(x)], x, d)
}
}
}
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